Typical beam splitters consist of a surface that reflects a portion of the incident light and transmits much of the remaining light. Knowledge and control of the ratio of the reflected to transmitted beams is important for power monitors and for interferometers as well as in other applications. If the polarization of the incident light is unknown or varies, then the polarization dependence of the beam splitter may limit the accuracy of the splitting ratio.
It is well known how to estimate the reflection and transmission of light for oblique incidence on an interface between two media. General formulas for the TE and TM polarization cases are known as Fresnel Equations. See, for example, J. M. Bennett and H. E. Bennett, "Polarization", Handbook of Optics, W. G. Dricoll, Ed. (McGraw-Hill, 1978) ISBN-0-07-04710-8.
The terminology, TE and TM, is not commonly used with regard to Fresnel Equations. "Transverse-Electric" and "Transverse-Magnetic" describe which field is perpendicular both to the plane of incidence and to the Z-axis; the Z-axis is chosen so that it is perpendicular to the plane of the interface, so that it is in the plane of incidence.
In older optics texts the subscripts, s and p, "senkrecht" and "parallel" are used in this connection. The equations invariably show that the s and p (TE and TM) reflectivities are different, with the s (TE) reflection being the larger. For example, for light incident at 30 degrees at an air-glass interface, the intensity reflection coefficients are 5.74% and 2.51%.
Metallic coatings show polarization dependence when used as beam splitters. Intuitively, for metallic conductors, the coating is so thin it can be thought of as conductive islands or droplets of dimensions small compared to the wavelength of light. These reflects the light by reradiating as if they were tiny dipole radiators. The effective orientation of the dipoles depends upon the polarization of the existing radiation, and, thus, the reflection is not polarization independent.
Another complication for slab beam splitters used with beams having random polarization is the undesirable reflections from the second surface. Two approaches commonly used to minimize effects of reflections from the second surface are less than ideal. The two faces are sometimes not mutually parallel so their reflections may be separated; utilizing a stop to remove the undesired reflection results in a polarization-dependent loss. The other approach is to produce an anti-reflection coating. However good, anti-reflection coatings that are polarization independent for oblique incidence are difficult to make.
To obtain a practical appreciation of the polarization dependence of typical metal coatings, we measured the ratio of reflected to transmitted light of a commercial calibrated circular gradient neutral density disk using 6828 .ANG. light incident at 45 degrees. FIG. 1 shows our results. Curve A(C) is for TE(TM) polarization. Curve B is for a linear polarization at 45 degrees to the plane of incidence, and is probably representative of the values that would be obtained if unpolarized light had been used. Notice that the polarization dependence is consistently larger than 4 db.
Thus, conventional beam splitters do not provide accurate power division when used with beams having random polarization.